Making a 

RECITATION 
SCHEDULE 



BOWDEN 



Making a 
Recitation Sdiedule 



BY 



JOSEPH BOWDCN, Ph. D. 
Professor of Mathematics in Adelphi College 



e^ 



New York 

Joseph Bowden 

24 Clifton Place, Brooklyn 

1922 






Copyright, 1922 

BY JOSEPH BOWDCN 



THf CANAAN P«!HTING CO. 
CANAAN, CONN. 

©.£1A685090 

SEP 'y[ ^^ n>. / 



List of Illustrations 



c3 


Page 


Sequence card _ - - 


6 


Electiv blank _ _ _ 


10 


Courses arranged by teachers 


11 


Courses arranged by departments 


12 


Clas list and conflict strip 


14 


Clas list table _ . . 


17 


Conflict table, partly made out 


23 


Conflict table 


26 


Course sequence form of schedule 


31 


Unary form of schedule 


• 34 



Making a Recitation 
Schedule 

1. The plan described in this little 
book makes the work of schedule mak- 
ing almost mechanical and thus does 
away with many of the worries gener- 
ally associated with such work. The 
plan is especially suitable for a small 
institution, but may be adapted to a 
large one, as wil be explaind later 
(§42). For large institutions however 
other methods may be more convenient. 



6 MAKING A 

Sequences. 2. One of the first 

things for the schedule maker to do is 
to divide the hours that may be used for 
clas work into separate groups, prefer- 
ably so that no two hours of a group 
come on the same day. I wil call these 
groups sequences. The sequence card 
used for several years at Adelphi Col- 
lege is given below: 

Sequence Card 





9^V Ml 1 10 1 11 


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1 . .( 1 4 


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RECITATION SCHEDULE 7 

The letters in the left hand colum 
stand for the days of the school week; 
the numbers across the top of the table 
indicate the recitation hours. Sequence 

I comes at the hours indicated by the 
figure 1 inside the table, and so on. The 
vacant hour on Monday at 3 o'clock is 
left for the faculty meeting and glee 
club rehearsal, the hour on Thursday at 

II for the general college assembly. 

Each course is to be assignd to hours 
coming all at one sequence. If the 
courses ar all three hour courses, each 
sequence should contain three hours. If 
ther ar some one or two hour courses, 
they may each be assignd to one or two 
hours of a three hour sequence. If ther 
ar some courses of more than three 
hours, some of the sequences may be 
made up of the corresponding numbers 
of hours or such a course may be as- 
signd to more than one three hour se- 
quence. For the latter purpose it may 
be convenient, for example, to call a six 
hour course two courses and to assign 
one of these hypothetical two courses to 



8 MAKING A 

one sequence and the other to another 
sequence. 

3. Just as the hours ar groupt into a 
number of sequences, so it would be 
convenient if it wer possible to arrange 
the courses into the same number of 
groups, such that no two courses of the 
same group should hav any common 
member, teacher or pupil. 

This requirement is frequently im- 
possible to realize. Then we try to real- 
ize it as nearly as possible, that is, we 
try to arrange the courses into groups so 
that any two courses of the same group 
do not hav the same teacher and hav as 
few pupil members in common as 
possible. 

If the number of sequences available 
is large enuf, it is possible to fulfil the 
above ideal condition exactly, if in no 
other way, by having one sequence for 
each course. 



RECITATION SCHEDULE 9 

A large number of sequences has the 
advantage, then, of removing conflicts, 
but the disadvantage of extending the 
hours of recitation into the late after- 
noon hours, if that is a disadvantage. A 
small number of sequences has the ad- 
vantage of closing the hours of recita- 
tion early in the day, but the disadvan- 
tage frequently of causing a large num- 
ber of conflicts, so that many students 
would hav to substitute for conflicting 
courses some courses that they do not 
wish or that ar not so wel suited to the 
ends they hav in view. 



Teachers' 4. The next thing, pos- 

Offers. sibly the first, for the pro- 
gram maker to do is to get from each 
teacher a list of the courses he offers for 
the next semester and a statement of 
any preferences he may hav for the 
hours of his courses. For this purpose 
the following form may be used : 



10 








MAKING A 

ElecNv Blank 

ADELPHI COLLEGE 


to the 

EDULE 


IVill you please fill out the Jorm printed beloTu and teturr 
office on or before 

COMMITTEE ON SCH 


Name 


COURSES FOR THE Is. 2nd SEMESTER 191 -191 


^-.^. l-S-l ^^.crcc... U%.!:S=Si. 


^^. 




5 

S 


H 




1 


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1 








L 


















M 




























5 


H 1 

L 

m{ 


— — 






















1 










1 


H 

L 
M 

















































2 I i 



The H, L, M in this form stand res- 
pectivly for History and Filosofy, Lan- 
guages and Literatures, Mathematics 
and Siences, the three divisions into 
which the courses oif erd in Adelphi Col- 
lege wer groupt, one of which divisions 
was chosen by each student as a major, 
another as an intermediate, and a third 
as a minor. 



RECITATION SCHEDULE 



11 



5. When these blanks ar returnd to 
the offis, they should be arranged alfa- 
betically according to the names of the 
teachers. In the upper left hand corner 
should be placed an abbreviation of the 
teacher's name, say the first one, two, 
or three letters of his last name, or some 
other symbol to represent the teacher. 

6. From these blanks a list of all 
courses offerd should be made out in two 
torms, first arranged alfabetically ac- 
cording to the names of the teachers 
and second according to the names of 
departments or subjects, either in one 
alfabetical list or in as many as ther ar 
divisions. The following may be used: 



Courses arranged 

By 
Teachers 



Ist 2nd 
semester 
192 -192 





HcLTne of 


of Courses 







































12 



MAKING A 



Courses Arranged i** 2nd 

By semester 

Departments 1^2 .192 





o-f Courses 

































Posting 
Courses. 
Students' 
Electivs. 



7. A list of all courses 
offerd should then be 
posted, or printed and dis- 
tributed among the stu- 



dents, for which purpose either of the 
latter forms, or a combination of them, 
may be used. From this list the stu- 
dents should make their selections, for 
reporting which the form used for the 
teachers* offers (§4) may be used. 



RECITATION SCHEDULE 13 

8. When the students' electiv blanks 
hav been handed in, they should be 
numberd, in the upper left hand corner, 
using say the numbers 1-50 for the 
seniors, 51-100 for the juniors, 101-200 
for the sofomores, 201-300 for the fresh- 
men. If the members of the freshman 
clas ar not individually known, we may 
assign the number 201 to the whole 
freshman clas, or 201 and several fol- 
lowing numbers to represent several 
types of freshmen. 

Clas 9. After evident errors 

Lists. in these blanks hav been 

corrected by the schedule committee, 

the clas lists should be made from them. 

For this purpose the following form may 

be used: 



14 



MAKING A 





^Cus List ^ 

o ^ AND ^ 
CohlFLlCT I 

J Strip | 






1 J 






/ 

2 

3 

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6 
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Stu^^yits Covf/icts 





RECITATION SCHEDULE 15 

In this form the small numbers in the 
left hand colum ar the students' serial 
numbers. For the sake of illustration I 
hav imagind a very small college with 
sixteen students. The large numbers at 
the right stand for eight courses which 
ar supposed to be offerd in our imagin- 
ary college. The use of these numbers 
wil be explaind later (§18). The left 
hand margin when fild out as explaind 
below (§§11, 12) wil be a clas list; the 
right hand margin when properly fild 
out (§§21-26) wil be the conflict strip of 
the corresponding clas. 

10. Either the students' names 
should be printed on the form after their 
serial numbers or the numbers and 
names should be printed on long strips 
of paper, using the same sized type and 
the same spacing as in the form. 

11. In making the clas lists one of 
these clas list blanks is used for each 
clas. The name of the course is ritten at 
the top of each blank as indicated. The 
blanks ar arranged alfabetically accord- 
ing to the names of the classes and ar 



16 MAKING A 

placed one on top of the other, the 
blank belonging to the first clas at the 
bottom, so that only the left hand mar- 
gins sho, except for the top one, which 
of course wil be entirely visible, and for 
the bottom one, of which the left hand 
colum of numbers should also be visible. 

The blanks wil be arranged more ac- 
curately in place if they ar laid on a 
drawing board upon which a line has 
previusly been drawn to correspond to 
one of the hevy black lines near the top 
of the clas list blank. As a blank is laid 
down, the hevy line on the strip should 
be made to match the line on the board 
and the blank should then be secured in 
place by two thum tacks, one at the top 
and one at the bottom. 

12. To make the clas lists a ruler is 
laid across the blanks from the middle 
of the first figure 1 to the middle of the 
second, the electivs of student number 1 
ar red from his electiv blank, and a 
broken line is drawn in pencil as indi- 
cated in the following diagram, which 
supposes that student 1 elects courses 
Bi. 2, Eng. 2, Hist. 2, and Mus. 2 ; and so 
on for each student. 



RECITATION SCHEDULE 



17 



Clas List Table 



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in 




^CusLisT 1 

I Conflict ^ 
1 Strip I 


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9 

10 

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11 
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NiL-m of NuTtlof- 

StudeiftS CofifliCtS 





























In this table each horizontal line in- 
dicates the corresponding student's 
choice of courses and each colum repre- 
sents the clas list of the corresponding 
course. 



18 MAKING A 

13. The clas lists should now be 
copied by placing a clas list blank be- 
side each of these clas lists in turn and 
checking the corresponding numbers. 



14. The copies should be given to 
the proper teachers for revision. When 
the revised lists ar returnd, the originals 
should be corrected and the lines re- 
drawn in ink, using preferably a ruling 
pen and making broad lines. 



Sections. 15. It may now be de- 

cided which courses should not be given 
and which classes divided into sections. 
The actual division into sections may be 
made now, according to any plan, or it 
may be left to be determind by the stu- 
dents* cards, each student being put into 
that section which suits his card best. 
The latter plan wil frequently be found 
more convenient. 



The number of laboratory sections 
may also be decided upon. 



RECITATION SCHEDULE 19 

Numbering 16. If the division into 

Classes. recitation and laboratory 
sections is made now, ther should be 
assignd to each recitation section and to 
each laboratory section a clas list and 
conflict strip. The classes and sections 
should also be numberd in series. For 
example, if Fysics 1 has two recitation 
sections and two laboratory sections, 
these sections may be numberd 71, 72, 
73, 74. 

If the division into sections is left to 
be made later, one serial number should 
be assignd to each clas, but no extra 
numbers for the sections. 

17. We may also assign numbers to 
courses which for varius reasons, as 
smallness of classes, it is believd wil not 
be given. Sometimes it is finally de- 
cided to giv such courses. In such case, 
if a number had not been assignd, we 
might be obliged to use decimal frac- 
tions, or letters, for interpolation, in 
order to hav the courses numberd in the 
proper order. ' 



20 MAKING A 

18. The assign d. numbers should be 
enterd, in red ink, above the correspon- 
ding numbers in the lists of courses men- 
tiond in §6. They should also be en- 
terd, in red ink, in three places on each 
clas list and conflict strip, in the two 
places indicated near the beds of the 
two colums on the left and right and 
also in the square to the right of the 
corresponding black number at the right. 

19. The strips belonging to courses 
which it is believd wil not be given may 
now be laid aside, to be used later, if it 
is decided to giv these courses. 

Conflicts. 20. We ar now redy to 
investigate conflicts. Two 'classes ar 
said to conflict if they hav either the 
same teacher or one or more pupils in 
common. Two such classes cannot be 
placed at the same sequence unless, in 
case the teacher causes the conflict, an- 
other teacher is assignd to one of the 
classes, or, in case the conflict is due to 
common pupils, these pupils choose be- 
tween the two courses. 



RECITATION SCHEDULE 21 

21. Arrange the clas lists again as 
in the table of §12. Take the first clas 
list from the bottom of the pile and lay- 
it alongside of each other clas list in 
turn. It is then easily seen whether clas 
1 and any other clas, say clas 2, hav any 
pupils in common, and, if so, how many, 
and which ones. 

If they hav none, rite an "0" with 
ink in the blank conflict strip of the first 
clas in the square opposit 2. 

If they hav more common members 
than the greatest number of conflicts 
that would be allowd, say 5, rite a check 
mark " v^" with ink in the square. 

If they hav less than 5 common mem- 
bers, we may follow either one of two 
plans. We may rite in the square with 
pencil the number of common members, 
or we may rite with ink the ordinal num- 
bers of the common members. The lat- 
ter plan takes more time, but wil fre- 
quently save time in the later work, 
since we frequently want to kno not only 
how many common members two classes 
hav, but who these conflicting members 
ar. 



22 MAKING A 

In this way all the squares of the 
blank conflict strip of clas 1 wil be fild, 
starting with the square opposit 2. 

In the same way all the squares of the 
second blank conflict strip, starting with 
the square opposit 3, may be fild. And 
so on. 

22. Of course, if two classes hav the 
same members, their conflicts with the 
other classes wil be the same. It wil not 
therfor be necessary to compare them 
both with the other classes. The squares 
of the second's blank conflict strip may 
be fild by copying from the first's strip. 

23. As the blanks ar fild out, lay 
them in a pile with the first at the top 
and the conflict strips showing, as indi- 
cated on the next page : 



RECITATION SCHEDULE 



23 



Conflict Tabic 

Partly made out 



■*>. 

^ 


fClASLlST I 
^ AND ^ 

^ cowflict ^ 
4 Strip ^ 


p5 






1 




5: 


^0 


^ 

^ 

rj 
S 


/ 


J J 


/ 


X 


3 


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^~ 


^ 


7 


^' 


— 1 

M 

1 


X 
3 

9 

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1 


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X 


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X 














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X 


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6- 


7 


2. 


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3 


5 


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7 


Stude7?r5 Conflicts 









































24 MAKING A 

24. We may now very easily enter 
in this table the conflicts due to teachers. 
If teacher A has courses 1, 2, 3, 4, an 
"A" should be enterd in squares 2, 3, 4 
on blank 1, in squares 3, 4 on blank 2, 
and square 4 on blank 3. Similarly for 
the other teachers. 

25. The blanks now constitute as 
laid together half of the conflict table. 
Since the conflicts of one clas with a 
second ar the same as those of the sec- 
ond with the first, this table should be 
symmetrical about the principal diagon- 
al, the line of red figures running from 
the upper left hand corner to the lower 
right hand corner. 

The blank squares of the first ro may 
therfor be fild by turning the first 
conflict strip around thru a right angle 
and laying its squares alongside of the 
first ro of squares. The blank squares 
of the second ro may similarly be fild 
by using the second conflict strip, and 
so on. 



RECITATION SCHEDULE 25 

26. The number of different courses 
that each course conflicts with should 
now be counted up and enterd in the 
square at the bottom of the correspond- 
ing conflict strip. These numbers may 
be cald the conflict coefficients. A course 
whose conflict coefficient is large is in 
general harder to arrange for on the 
schedule than one whose coefficient is 
small. The courses with largest coeflft- 
cients should therfor be provided for 
first. 

27. If the conflict strips ar now 
again arranged as in §23, altho this is 
not necessary for our purpose, they wil 
form the completed conflict table, which 
wil look as follows: 



26 



MAKING A 

Conflict Table 





\Cus List \ 

I Conflict | 
^ Stbip i 

06 c^ 


\ 

/£ 




i 


^ 

1 






01 




/ 


J J 


/ 


X 


3 


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T 


7 


?■ 




/ 

X 
3 

5- 

7 

10 

1 1 
12. 
/3 


/ 


/ 


x> 




3 


t, 


7 


z 


^ 


iT 


X 





2. 


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(y 


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5" 


3L 





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Hu.rK of - Num of 
Stii.clent^ ConfhctS 


7 


7 


7 


7 


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7 


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7 

























RECITATION SCHEDULE 27 

28. It may be wise now to make a 
vertical list of the courses on one sheet 
of paper, arranging the courses accord- 
ing to the magnitude of their conflict 
coefficients. 

Assigning 29. The object now is 

Courses to arrange the courses in 

to groups, such that the 

Sequences, courses of each group do 

not conflict with each other, or conflict 

as little as possible, and to assign these 

groups to separate sequences. All of 

our previus work has been done in order 

to make this work as easy as possible. 

Probably the best plan is to cut the 
conflict strips from the completed clas 
list and conflict strips. Place the clas 
lists aside. 

If the division into sections has been 
left to be determind by the students' 
cards (§15), the conflict strip belonging 
to a clas which is to hav sections should 
now be assignd to recitation section 1 
and another conflict strip should be 
made out for each other recitation sec- 
tion and laboratory section by copying 
from this strip. 



28 MAKING A 

The conflict strips should be placed 
side by side on a table, arranged ac- 
cording to the magnitude of their con- 
flict coefficients. 

Now take as many blank clas list and 
conflict strips as ther ar sequences and 
from each of these cut out the strip con- 
taining the list of course numbers. 
Number these strips to correspond to 
the sequences, say from 1 to 12. We wil 
call these strips, so numberd, the 
sequence gides. Spred the sequence 
gides out on a table, leaving spaces be- 
tween to represent the sequences. 

30. We may next assign certain 
courses or sections arbitrarily to the se- 
quences, not more than one *to each, 
these courses or sections being ones 
which for varius reasons it seems should 
be set at definit places on the program. 
The corresponding conflict strips should 
be placed beside the proper sequence 
gides. 

31. Now take up the conflict strip 
belonging to that one of the unassignd 



RECITATION SCHEDULE 29 

courses or sections whose conflict coeffi- 
cient is greatest or one of the greatest. 
Say this is course 9. By running the eye 
along the 9th ro of squares on the strips 
belonging to the courses alredy assignd 
it can generally be easily seen at which 
sequence course 9 should be placed to 
cause the least number of conflicts. 
Place this conflict strip in the space 
representing this sequence. 

If ther ar several equally available 
sequences, it is usually best to put the 
course at the sequence coming earliest 
in the day. Or this course can be left 
to be assignd after the course having 
the next highest conflict coefficient. 

We may continue in the same way 
until all the courses and sections hav 
been assignd to sequences, the conflict 
strips for each sequence being arranged 
in numerical order. 

32. If it happens that about the 
same number of conflicts wil be caused 
by assigning a course to either of two 
different sequences, it may be advisable 
to consider who ar the students that 



30 MAKING A 

cause the conflicts. One student may 
find it easy to change his electivs, an- 
other may find it hard. 

If the conflict table was made accord- 
ing to the first plan mentiond in §21, it 
wil now be advisable to reconstruct a 
part of it according to the second plan. 
Suppose that courses 2, 4, 5, and 7 ar 
alredy assignd to a certain sequence 
and we wish to find what conflicts wil be 
caused by putting course 6 at this 
sequence. We compare clas list 6 again 
with clas lists 2, 4, 5, and 7 and rite with 
ink the ordinal numbers of the students 
causing the conflicts in the correspond- 
ing squares of the conflict strips 6, 2, 4, 
5, 7 in place of the numbers originally 
put in these squares. 

33. When a clas is assignd to a se- 
quence, corresponding entries should be 
made, in pencil, in the course sequence 
form of schedule, the sequence room 
schedule, and on the teacher's hour time 
card. 

The form for the last of these may be 
the same as that given for the sequence 



RECITATION SCHEDULE 



31 



card in §2. A form for the first is given 
below. In the interior squares should 
be placed the numbers of the courses 
coming at the varius sequences. 



Course Sequence 
rorm of 
Schedule 



1st 2nd 
semester 
192 -192 





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Dr 


























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Ea 


























E.^ 


























Fil 


























Tys 


























Tr 


























Geol 


























Ger 


























Grk 


























Hisf 


























It 


























hat 


























Uaih 


























Uus 


























Fsy. 


























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32 MAKING A 

34. The sequence room schedule 
differs from the course sequence form of 
schedule in having inserted in the 
squares of the left hand margin the 
numbers of the rooms insted of the 
names of departments. In the interior 
squares should be placed the names of 
the teachers (or classes) occupying the 
varius rooms at the varius sequences. 

35. After all courses hav been as- 
signd to places it wil frequently be 
found that certain courses hav more 
conflicts than v^hen first assignd to 
places. The conflicts hav been heaping 
up as the time table grew. It wil be 
wise to consider each course over again, 
to see if, by changing its .assignment, 
the number of conflicts cannot be re- 
duced. Frequently, when one course 
has its assignment changed, an opening 
is made by which we may improve the 
assignment of another course. The 
opening, if any, is of course in the se- 
quence from which the first course has 
been removed. While making these 
changes, also, the teachers' cards should 



RECITATION SCHEDULE 33 

be studied, to see if they cannot be im- 
proved. 

36. It wil be wise now to enter the 
electivs chosen by the students in the 
sequence strips at the bottoms of their 
electiv blanks. If these electiv blanks 
ar arranged one above another leaving 
the sequence strips exposed, it wil some- 
times be evident that one clas, senior, 
junior, sofomore, or freshman, has been 
favord more than the others with early 
hours. Sometimes a change can be 
made so as to remove the inequality. 

Sequence 37. These sequence 

Time time cards of the students 

Cards. may also be used in inves- 
tigating what course a student had bet- 
ter be advised to take in place of one of 
two conflicting courses. 

38. They may also be used, vrith the 
sequence time card of the teacher, to 
determin the best place for some new 
course which it may hav been decided 
to giv. 



34 



MAKING A 



Forms 39. The time table is 

of now complete and exists 

Schedule in several forms. It may 
also be put into several other forms con- 
venient for use, one of which follows: 



Unciry Torrn 
of Schedule 



. semester 
192 -192 



Hist anj)Vi l 


LaNQ an:dL\T 


H^THAHI)S\ 


Couy-se 


5.^ 


Tch^ 


■Rm 


Course 


Ser 


Tchr \-R'" 


Course 


Se^ 


n-kr 


n^ 






















1 






















-A 


1 



























40. From the schedule in the above 
form it may be wise to pick out the 
courses open to freshmen and. with these 
make a freshman schedule in the same 
form. 



41. Sometimes tables showing what 
courses come at the varius hours of the 
week and what teachers occupy the 
varius rooms at the varius hours of the 
week ar useful. These of course can be 
compiled from the other tables. 



RECITATION SCHEDULE 35 

Large 42. The plan describ- 

Institutions. ed in this book would be 
unwieldy for a large institution. But 
it might be applied by artificially divid- 
ing the large institution into several 
small ones. 

The time table might be made up first 
for a certain group of students, say 
those whose chief work is in sience. 
Then another group of students would 
be considerd, the courses that they hav 
in common with the first group being 
considerd as fixt in place. 

The first group to be considerd might 
be the senior clas, the second the junior 
clas, etc. 

43. The work may also sometimes 
be simplified by considering insted of 
hidividual students groups of students 
whose work is the same. A single num- 
ber could represent such a group. 

Examination 44. It wil be evident 
Schedule, that the same method 
may be applied to making an examina- 
tion schedule, or the examination sche- 
dule can be made up from the recitation 
schedule. 



INDEX Article 

Adjusting schedule - - - - SI 
Assigning courses to sequences - 29-32 

Clas list and conflict strip - . . 9 

Clas lists - - . . 9, 11, 12 

Clas list table 12 

Conflict coefficients .... 26 

Conflicts - - - . . - 20 
Conflict strips - ... 9, 21-27 

Conflict table 27 

Copying clas lists - - - - 13 

Correcting errors in electiv blanks - 9 

Course sequence form of schedule - 33 

Courses arranged by departments - - 6 

" teachers - - 6 

" to be divided into sections - 15 

" " omitted ... 15 

Electiv blanks 8 

Examination schedule ... 44 

Freshman " . . . _ 40 

Hour time cards - - - - - 33 

Laboratory sections - - - - 15 

Method applied to large institution - 42 

Numbering classes - - - - 16 

" students' electiv blanks - 8 

Posting list of courses _ . _ 7 

Revising clas lists .... 14 

Sequences _ . . _ _ 2 

Sequence gides - . - _ 29 

" room schedule - - - 34 

strips - . - - 36 

*' time cards . - . 37 

Students' electivs - . - - 7 

Teachers* offers ... . 4 

Unary form of schedule - - - 39 



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